int dx / (x^2 +4x+20)^(3/2)

please guide me here.

Question

int dx / (x^2 +4x+20)^(3/2) 

please guide me here.

turingtest · Answer

again: trig substitution

turingtest · Answer

complete the square first...

turingtest · Answer

@lilMissMindset do you know what I mean?
are you stuck somewhere?

anonymous · Answer

why cant i do it? T.T

turingtest · Answer

I don't know, where are you stuck?
what did you get after completing the square?

anonymous · Answer

i used trig substitution. and then i became so confused with the exponent 3/2

turingtest · Answer

the term in the denominator will be som trig sub squared if you do it correctly, which when raised to the 3/2 power becomes that trig function to the third, since$$(x^2)^{3/2}=x^3$$

anonymous · Answer

yes! yes! i think i am getting it already. thank you again and again for being patient with me.

turingtest · Answer

let me know if you get stuck again :)

anonymous · Answer

i got the answer. thank you again.